Support Effect of Boron Nitride on the First N-H Bond Activation of NH3 on Ru Clusters

Support effect is an important issue in heterogeneous catalysis, while the explicit role of a catalytic support is often unclear for catalytic reactions. A systematic density functional theory computational study is reported in this paper to elucidate the effect of a model boron nitride (BN) support on the first N-H bond activation step of NH3 on Run (n = 1, 2, 3) metal clusters. Geometry optimizations and energy calculations were carried out using density functional theory (DFT) calculation for intermediates and transition states from the starting materials undergoing the N-H activation process. The primary findings are summarized as follows. The involvement of the model BN support does not significantly alter the equilibrium structure of intermediates and transition states in the most favorable pathway (MFP). Moreover, the involvement of BN support decreases the free energy of activation, ΔG≠, thus improving the reaction rate constant. This improvement is more obvious at high temperatures like 673 K than low temperatures like 298 K. The BN support effect leading to the ΔG≠ decrease is most significant for the single Ru atom case among all three cases studied. Finally, the involvement of the model BN may change the spin transition behavior of the reaction system during the N-H bond activation process. All these findings provide a deeper insight into the support effect on the N-H bond activation of NH3 for the supported Ru catalyst in particular and for supported transition metal catalysts in general.


Introduction
Bockris introduced the concept of a "hydrogen (H 2 ) economy" envisioning an energy transition founded on the utilization of H 2 as a vector for the generation of clean and environmentally sustainable energy [1].Over recent decades, the production of H 2 from various sources, its transport and storage, and finally its use have been extensively investigated [2].H 2 has assumed a prominent role in the energy sector, finding applications in stationary power generation, transportation, and as an energy vector for storing surplus electrical energy generated during off-peak periods [3].However, one of the challenges in H 2 technology today is storage and transportation.Due to the problems of physical storage methods, chemical storage methods based on using another easily transportable hydrogen-containing compound, which in turn produces H 2 by chemical reaction, may be more favored.Ammonia (NH 3 ) is currently one of the most promising H 2 carriers.It can form a liquid at low pressure at ambient temperature, it is easy to transport and store, and its industrial synthesis is mature.If the cost-effective production of H 2 through NH 3 decomposition can be achieved, it is anticipated that H 2 storage and transportation via NH 3 will exhibit significant technical and economic competitiveness.
In recent years, NH 3 decomposition to produce H 2 has received more and more attention by people in fundamental research and industrial applications [4][5][6][7][8][9][10][11][12].Because of the inertia of NH 3 , its activation and conversion to N 2 and H 2 has to involve catalysis.The activation of the N-H bond is one of the key steps as well as the first step in the catalytic conversion of NH 3 .The activation mechanism of the N-H bond is undoubtedly important for understanding the existing NH 3 catalytic conversion processes and developing new NH 3 catalytic conversion systems.Supported nickel (Ni) and supported ruthenium (Ru) catalysts are the most commonly used catalysts in fundamental research and in pilot plants [4,5,[8][9][10][11][12].Many researchers have studied the reaction kinetics or/and reaction mechanisms of NH 3 decomposition catalyzed by Ru-or Ni-based catalysts [12,13].Yue et al. [14] summarized several ways of the N-H bond activation on metal catalysts.They also proposed that the difficulty of N-H bond activation of NH 3 is due to the relatively large N-H bond energy and the relative activity of the lone pair of electrons on the N atom.However, these mechanistic point of views focused on reactions of organic synthesis.Piers et al. [15] reported the N-H bond activation of NH 3 via reaction with low-valence molybdenum complexes of a diborate pentadentate ligand system.
In a broader scope of the NH 3 decomposition mechanism on transition metal catalysts, most of the research has been carried out with a plane surface model like Pd(111) [16], Ni(111), Co(111), Fe(110) [17], Cu(111) [18], Cu(100) [19], and WC(0001) [20].For example, Jiang et al. [16] reported that NH is the most abundant intermediate on the Pd (111) surface and the dehydrogenation of NH 3 is the rate-determining step in the overall reaction.However, the kinetic analysis and mechanistic studies of NH 3 decomposition on Ni and Ru catalysts have not yet led to being clearly studied in detail [21].Especially, the activation of N-H bonds on the metal atom/clusters is still not well understood, at the level of elementary steps and at the molecular level [4,22,23].For example, a well-recognized reaction pathway of NH 3 decomposition can be expressed as described in Scheme 1 [24].
Molecules 2024, 29, x FOR PEER REVIEW 2 of 21 its industrial synthesis is mature.If the cost-effective production of H2 through NH3 decomposition can be achieved, it is anticipated that H2 storage and transportation via NH3 will exhibit significant technical and economic competitiveness.
In recent years, NH3 decomposition to produce H2 has received more and more attention by people in fundamental research and industrial applications [4][5][6][7][8][9][10][11][12].Because of the inertia of NH3, its activation and conversion to N2 and H2 has to involve catalysis.The activation of the N-H bond is one of the key steps as well as the first step in the catalytic conversion of NH3.The activation mechanism of the N-H bond is undoubtedly important for understanding the existing NH3 catalytic conversion processes and developing new NH3 catalytic conversion systems.Supported nickel (Ni) and supported ruthenium (Ru) catalysts are the most commonly used catalysts in fundamental research and in pilot plants [4,5,[8][9][10][11][12].Many researchers have studied the reaction kinetics or/and reaction mechanisms of NH3 decomposition catalyzed by Ru-or Ni-based catalysts [12,13].Yue et al. [14] summarized several ways of the N-H bond activation on metal catalysts.They also proposed that the difficulty of N-H bond activation of NH3 is due to the relatively large N-H bond energy and the relative activity of the lone pair of electrons on the N atom.However, these mechanistic point of views focused on reactions of organic synthesis.Piers et al. [15] reported the N-H bond activation of NH3 via reaction with low-valence molybdenum complexes of a diborate pentadentate ligand system.
In a broader scope of the NH3 decomposition mechanism on transition metal catalysts, most of the research has been carried out with a plane surface model like Pd(111) [16], Ni(111), Co(111), Fe(110) [17], Cu(111) [18], Cu(100) [19], and WC(0001) [20].For example, Jiang et al. [16] reported that NH is the most abundant intermediate on the Pd (111) surface and the dehydrogenation of NH3 is the rate-determining step in the overall reaction.However, the kinetic analysis and mechanistic studies of NH3 decomposition on Ni and Ru catalysts have not yet led to being clearly studied in detail [21].Especially, the activation of N-H bonds on the metal atom/clusters is still not well understood, at the level of elementary steps and at the molecular level [4,22,23].For example, a well-recognized reaction pathway of NH3 decomposition can be expressed as described in Scheme 1 [24].Scheme 1.A reaction mechanism described by Sun in Ref. [24] and the references therein.Scheme 1, as described by Sun in Ref. [24] and the references therein, outlines a reaction mechanism in which the symbol "*" designates the reactive site responsible for NH3 decomposition.The initial two steps within Scheme 1 correspond to the initial activation of the first N-H bond in NH3 on a specific catalytic site.However, the comprehensive understanding of the reaction mechanism presented in Scheme 1, particularly within these initial two steps, remains elusive.This holds especially true for critical information regarding the nature of the catalytic site represented by "*".Several unresolved questions come to light, particularly concerning these initial two steps in Scheme 1.For example, firstly, it is not clear whether the two "*" notations in the first two steps correspond to the same metal site or two different metal sites.It should be noted that the answer may be Scheme 1.A reaction mechanism described by Sun in Ref. [24] and the references therein.Scheme 1, as described by Sun in Ref. [24] and the references therein, outlines a reaction mechanism in which the symbol "*" designates the reactive site responsible for NH 3 decomposition.The initial two steps within Scheme 1 correspond to the initial activation of the first N-H bond in NH 3 on a specific catalytic site.However, the comprehensive understanding of the reaction mechanism presented in Scheme 1, particularly within these initial two steps, remains elusive.This holds especially true for critical information regarding the nature of the catalytic site represented by "*".Several unresolved questions come to light, particularly concerning these initial two steps in Scheme 1.For example, firstly, it is not clear whether the two "*" notations in the first two steps correspond to the same metal site or two different metal sites.It should be noted that the answer may be different when dealing with a single metal atom and with metal clusters.It is worth noting that the answer to this question may differ when considering a single metal atom as opposed to metal clusters.Secondly, there is a lack of understanding regarding how the incorporation of a catalytic support into the metal site alters the reaction behaviors.These questions are certainly important since catalytically active metal components are always resided on a frequently used support, like Al 2 O 3 , carbon nanotube, graphene, and boron nitride (BN).Support effect is an important topic in heterogeneous catalysis, in particular for Ru-catalyzed hydrogen utilization processes [25], and for NH 3 decomposition to obtain high-purity hydrogen [26].
To gain a clearer comprehension of the impact of catalytic support and metal cluster size on N-H bond activation behavior in metal atom/clusters, we present a DFT study of N-H bond activation of NH 3 on both of the unsupported and supported Ru atom/clusters in this paper.This paper focuses on the structural, energetic, and spin multiplicity changes during the N-H bond activation process without and with the model hexagonal BN support.BN, like its C analogue, can exist in various forms like hexagonal sheets, nanotubes, and nanobowls, resulting in various interesting properties and being useful in the field of catalysis [27][28][29].We found that the model support can change the structure of intermediates and transition states and decrease the reaction energy barrier.The results presented in this work offer valuable qualitative insights, contributing to a deeper understanding of the impact of catalytic support and metal cluster size on the activation of N-H bonds and other types of saturated bonds in a broader context.

Adsorption Energy of Ru n Atom/Clusters on the BN Support
Before studying the support effect of BN on the N-H bond activation process, the stability of Ru n clusters on the BN support should be first examined.In general, a transition metal center can have more than one accessible spin state, which can be close in energy to each other.In particular, as is well known, an isolated Ru atom has a ground state in its quintet (spin multiplicity, S = 5, denoted as 5 Ru) state since its ground state electron configuration is [Kr]4d 7 5s 1 .However, when an Ru atom interacts with other entities like a second Ru atom to form an Ru 2 cluster, or an NH 3 molecule for further reaction, it is possible to change its ground state spin multiplicity.The change in spin multiplicity is always not possible to increase, since the incorporation of another entity into an Ru atom lowers its symmetry.Similarly, when an Ru n cluster interacts with the BN support, the ground spin multiplicity may also change in principle.
Therefore, in order to calculate the adsorption energy of the Ru clusters on BN support, one needs to compare the energy of the Ru n clusters for both of the unsupported and supported cases with different spin multiplicities.All the species notations shown in the first column in Table 1 correspond to their ground states after a similar energy calculation process as the case of Ru 1 -BN.For instance, 5 Ru 1 -BN is considered as the ground state since its energy is lower than 1 Ru 1 -BN, 3 Ru 1 -BN, and 7 Ru 1 -BN. 9Ru 3 is considered as the ground state since its energy is lower than 1 Ru 3 , 3 Ru 3 , 5 Ru 3 , 7 Ru 3 , and 11 Ru 3 .In addition, the model BN sheet has a singlet ground state since a triplet BN sheet has a much higher energy.
Figure 1 shows the optimized geometries of 7 Ru 2 -BN and 9 Ru 3 -BN.Interestingly the two Ru atoms tend to stand perpendicular rather than lie parallel to the BN plane in 7 Ru 2 -BN.The triangular plane formed from the three Ru atoms also tends to stand perpendicular to the BN plane.Various initially designed structures were considered, such as placing Ru atom(s) at the center of a BN hexagonal ring, a B-N bridge site, as well as positions directly attached to a B or N atoms.These initial structures were subjected to geometry optimization to identify the most stable configuration.Notably, after optimization, the lowest-energy structure for all initially designed configurations featured Ru atoms positioned closer to B atoms, as shown in Figure 1.Table 1 shows that the adsorption energies (E ad < 0) of these Ru clusters on the BN sheet are moderately high, making the adsorption process feasible (G ad < 0).
(Ead < 0) of these Ru clusters on the BN sheet are moderately high, making the adsorption process feasible (Gad < 0).Table 1.Adsorption energy (Ead) and free energy at 298 K (Gad) of an Run cluster on the BN support.All the spin multiplicity indicated on the upper left of a species notation corresponds to the ground spin state.

Adsorption Process
Ead (kcal/mol) Gad (kcal/mol, 298 K) As mentioned above, since Ru1 has a quintet ground state, in this work the reaction behavior of the first N-H bond activation of NH3 on a 5 Ru atom was investigated in the beginning.Figure 2a presents the optimized geometries of the species participating in the NH3 and 5 Ru reaction ((R1) as defined in Section 3).The reaction commences with the isolated NH3 molecule and a 5 Ru atom, serving as the starting materials (designated as 5 SM-Ru1-unsup).As the reaction progresses, the NH3 molecule approaches the 5 Ru atom, resulting in the formation of the first energy minimum structure, denoted as 5 IM1-Ru1unsup, with an N…Ru distance of 2.460 Å. Concurrently, the N-H bond containing the detaching H atom (referred to as Ha hereafter) experiences a slight increase in length.Subsequently, 5 IM1-Ru1-unsup evolves into another intermediate, 5 IM2-Ru1-unsup, via a transition state structure denoted as 5 TS-Ru1-unsup.During this transition, Ha detaches from the N atom, moving closer to the Ru atom, while the N atom further approaches Ru.These structural alterations are evident in Figure 2a, where, for instance, the N…Ha distance increases from 1.016 Å in 5 IM1-Ru1-unsup to 1.599 Å in 5 TS-Ru1-unsup and then to 3.589 Å in 5 IM2-Ru1-unsup.In the 5 IM2-Ru1-unsup intermediate, the Ru-Ha bond is fully formed, as indicated by its length of 1.680 Å.As mentioned above, since Ru 1 has a quintet ground state, in this work the reaction behavior of the first N-H bond activation of NH 3 on a 5 Ru atom was investigated in the beginning.Figure 2a presents the optimized geometries of the species participating in the NH 3 and 5 Ru reaction ((R1) as defined in Section 3).The reaction commences with the isolated NH 3 molecule and a 5 Ru atom, serving as the starting materials (designated as 5 SM-Ru 1 -unsup).As the reaction progresses, the NH 3 molecule approaches the 5 Ru atom, resulting in the formation of the first energy minimum structure, denoted as 5 IM1-Ru 1 -unsup, with an N. ..Ru distance of 2.460 Å. Concurrently, the N-H bond containing the detaching H atom (referred to as H a hereafter) experiences a slight increase in length.Subsequently, 5 IM1-Ru 1 -unsup evolves into another intermediate, 5 IM2-Ru1-unsup, via a transition state structure denoted as 5 TS-Ru 1 -unsup.During this transition, H a detaches from the N atom, moving closer to the Ru atom, while the N atom further approaches Ru.These structural alterations are evident in Figure 2a, where, for instance, the N. ..H a distance increases from 1.016 Å in 5 IM1-Ru 1 -unsup to 1.599 Å in 5 TS-Ru 1 -unsup and then to 3.589 Å in 5 IM2-Ru 1 -unsup.In the 5 IM2-Ru 1 -unsup intermediate, the Ru-H a bond is fully formed, as indicated by its length of 1.680 Å.
Later, the PESs in the singlet, triplet, and heptet states (S = 1, 3, and 7, respectively) were also investigated in this work similar to the quintet PES case.Since the energies of the SM, IM1, TS, and IM2 species on the singlet and heptet PESs are significantly higher than the corresponding species on the triplet and quintet PESs, the results related to the singlet and heptet PESs will not be reported in this paper.The geometrical characters of the key species on the triplet PES (Figure 2b) are rather similar to the ones on the quintet PES.The primary differences are in that the N. ..Ru and the N. ..H a distances are often shorter in the triplet species than that in the quintet species for (R1).For example, the N. ..Ru distance is 1.985 Å in 3 TS-Ru 1 -unsup compared to 2.094 Å in 5 TS-Ru 1 -unsup, and the N. ..H a distance is 1.444 Å in 3 TS-Ru 1 -unsup compared to 1.599 Å in 5 TS-Ru 1 -unsup.
As described in Section 2.1, when an isolated Ru atom resides on a model BN surface to form Ru 1 -BN, quintet is still in the ground spin state compared to the singlet, triplet, and heptet states.Similar to the unsupported case of (R1) described above, the results related to the singlet and heptet PESs will also not be reported for the supported case of (R4). Figure 2c,d show that, except the incorporation of the BN support, the geometries of the Ru. ..NH 3 part are somewhat similar to the case of unsupported reaction system, with the main difference in that the N. ..H a distance in the TS for the supported case is slightly longer than that for the unsupported case.For example, the distance between the detaching atom of the H a and N atom in NH 3 in3 TS-Ru 1 -unsup is 1.444 Å (Figure 1b), which is 1.472 Å in 3 TS-Ru 1 -BN (Figure 2d) when the BN support is added to the reaction system.In addition, the distance between H a and Ru atoms becomes shorter after adding the model BN support.Later, the PESs in the singlet, triplet, and heptet states (S = 1, 3, and 7, respectively) were also investigated in this work similar to the quintet PES case.Since the energies of the SM, IM1, TS, and IM2 species on the singlet and heptet PESs are significantly higher than the corresponding species on the triplet and quintet PESs, the results related to the singlet and heptet PESs will not be reported in this paper.The geometrical characters of the key species on the triplet PES (Figure 2b) are rather similar to the ones on the quintet PES.The primary differences are in that the N…Ru and the N…Ha distances are often shorter in the triplet species than that in the quintet species for (R1).For example, the N…Ru distance is 1.985 Å in 3 TS-Ru1-unsup compared to 2.094 Å in 5 TS-Ru1-unsup, and

Energy Profiles
Figure 3a,b show the relative energy profiles for (R1) and (R4) undergoing on the quintet and triplet PESs, respectively.For (R1), 3 SM-Ru 1 -unsup is higher in energy than 5 SM-Ru 1 -unsup, which is not surprising since an Ru atom has a quintet ground state.model BN support.

Energy Profiles
Figure 3a,b show the relative energy profiles for (R1) and (R4) undergoing on the quintet and triplet PESs, respectively.For (R1), 3 SM-Ru1-unsup is higher in energy than 5 SM-Ru1-unsup, which is not surprising since an Ru atom has a quintet ground state.However, it is noteworthy that the intermediate IM1 has a triplet ground state rather than quintet.In another word, the ground spin state of Ru is changed during the course of an NH3 molecule approaching an Ru atom.More importantly, both the transition state TS and intermediate IM2 display lower energy on the triplet PES compared to the quintet PES.The activation energy of (R1), defined as the energy difference between TS-Ru1-unsup and IM1-Ru1-unsup, is also lower on the triplet PES (25.6 kcal/mol) than on the quintet PES (38.8 kcal/mol).Examining the energy profiles presented in Figure 3a reveals that IM1 proceeds much easier to TS on the triplet PES than on the quintet PES for (R1) ( 5 IM1-Ru1-unusp → Examining the energy profiles presented in Figure 3a reveals that IM1 proceeds much easier to TS on the triplet PES than on the quintet PES for (R1) ( 5 IM1-Ru 1 -unusp → 5 TS-Ru 1 -unusp vs. 3 IM1-Ru 1 -unusp → 3 TS-Ru 1 -unusp).However, considering that 5 SM-Ru 1 -unsup is much more stable than 3 SM-Ru 1 -unsup in energy, in this time it is still insufficient to verify the following hypothesis, named as Hypothesis A, i.e., (R1) operates on the triplet PES.On the basis of energetic data, Hypothesis A is valid if Hypothesis B is valid, that is, 5 IM1-Ru 1 -unsup can undergo spin transition to 3 IM1-Ru 1 -unsup with a low spin transition energy (lower than 5 IM1-Ru 1 -unsup going to 5 TS-Ru 1 -unsup).An exact calculation of such spin transition energy, belonging to a "spin-forbidden" process problem [30,31], can be achieved by the "minimum energy at crossing point (MECP)" method.Although in this work we did not calculate the MECP value for the 5 IM1-Ru 1 -unsup species, through two single-point energy calculations (the results are shown in Figure 4; see more explanation in its figure caption as well) and logical reasoning, Hypothesis B can be verified.Since the energy difference of b → b ′ is the MECP, which is certainly smaller than 4, the energy differences of points a → a ′ and c → c ′ are 19.6 and 5.5 kcal/mol, respectively, and thus the energy difference of b → b ′ , or MECP, is lower than 5.5 kcal/mol.This comparison consequently verifies that 5 IM1-Ru 1 -unsup (actually the same point as c) going to 3 IM1-Ru 1 -unsup (requiring less than 5.5 kcal/mol) is much easier than it going to 5 TS-Ru 1 -unsup (requiring 31.5 kcal/mol, see Figure 2a), that is, Hypothesis B is verified.Therefore, Hypothesis A is also verified.more explanation in its figure caption as well) and logical reasoning, Hypothesis B can be verified.Since the energy difference of b → b′ is the MECP, which is certainly smaller than a → a′ or c → c′ (Eb-b′ < Ea-a′, Eb-b′ < Ec-c′).From Figure 4, the energy differences of points a → a′ and c → c′ are 19.6 and 5.5 kcal/mol, respectively, and thus the energy difference of b → b′, or MECP, is lower than 5.5 kcal/mol.This comparison consequently verifies that 5 IM1-Ru1-unsup (actually the same point as c) going to 3 IM1-Ru1-unsup (requiring less than 5.5 kcal/mol) is much easier than it going to 5 TS-Ru1-unsup (requiring 31.5 kcal/mol, see Figure 2a), that is, Hypothesis B is verified.Therefore, Hypothesis A is also verified.The verification of Hypothesis A mentioned above shows we can use the concept of the most favorable pathway (MFP) to describe the reaction behavior of (R1).In the MFP energy profile, all key species are considered only with their ground state spin multiplicity.Figure 3c shows the energy profile of the MFP for (R1) deduced from Figure 3a, and correspondingly, the optimized geometries of the key species involved in the MFP for (R1) can be seen in Figure 2e.
In this work we have performed a similar verification process for all other reactions of (R2)~(R5).All of the six reactions in this work have an MFP.Hereafter in this paper, the structures and energy profiles are only reported for the MFPs, instead of presenting the results about all of the spin states.The verification of Hypothesis A mentioned above shows we can use the concept of the most favorable pathway (MFP) to describe the reaction behavior of (R1).In the MFP energy profile, all key species are considered only with their ground state spin multiplicity.Figure 3c shows the energy profile of the MFP for (R1) deduced from Figure 3a, and correspondingly, the optimized geometries of the key species involved in the MFP for (R1) can be seen in Figure 2e.
In this work we have performed a similar verification process for all other reactions of (R2)~(R5).All of the six reactions in this work have an MFP.Hereafter in this paper, the structures and energy profiles are only reported for the MFPs, instead of presenting the results about all of the spin states.
Similar to the unsupported case of (R1), Figure 3d shows the energy profile of the MFP for the BN-supported case of (R4), which is deduced from the two profiles in Figure 3b, and correspondingly, the optimized geometries of the key species involved in the MFP for (R4) shown in Figure 2f.A comparison between the results in Figure 3c,d reveals that the intermediates of IM1 and IM2 are obviously stabilized by ~14 kcal/mol when the BN support is involved.TS is lowered by ~15 kcal/mol, leading to the reaction energy barrier, is lowered from 25.6 kcal/mol for the Ru 1 -unsup case to 24.0 kcal/mol for the Ru 1 -BN case.The reaction barrier of (R4), i.e., the energy difference between 3 IM1-Ru 1 -BN and 3 TS-Ru 1 -unsup, is 24.0 kcal/mol, which is rather consistent with 1.066 eV (24.6 kcal/mol) for CNT-supported Ru 1 , as reported by Zhou et al. [32].The results in this work and in Ref. [32] show that Ru can be more effective than Pd for N-H bond activation, since the N-H bond activation barrier is 39.4 kcal/mol on Pd(111) [16].

Effect of the BN Model Size
Figure 5 show the optimized geometries of IM1 and TS involved in the first N-H bond activation of NH3 on the varied model BN-supported Ru1 ((R4) with different sizes of BN model sheet).To examine the rationality of the B19N19H16 sheet as a representative model BN sheet, we examined how the reaction barrier of (R4), i.e., energy difference of 3 IM1-Ru1-BN → 3 TS-Ru1-BN, changed with expanding and reducing the B19N19H16 sheet model.On one hand, we enlarged it to create a B26N26H18 sheet model, and on the other, we reduced it to a B15N15H14 sheet model.These three distinct sheet models were employed as BN support for structural optimization and energy calculations of the intermediates and transition states involved in the N-H bond activation process.The structural characteristics of IM1 and TS derived from these three sheet models exhibited remarkable similarity, as depicted in Figure 2f.Furthermore, the energy results displayed a high degree of consistency.The reaction barrier obtained for the three BN sheet models used as supports are 24.3,24.0, and 24.3 kcal/mol for B26N26H18, B19N19H16, and B15N15H14, respectively.These calculations unequivocally demonstrate that the BN models used in this work possess size consistency, thus validating the rationale behind utilizing the B19N19H16 sheet model for BN support calculations.Considering the computational complexity of this

Support Effect on the First N-H Bond Activation Process of NH 3 on an Ru 2 Cluster
Similar to the results about Ru 1 shown in Section 2.2, for all key species involved in the NH 3 activation process on an unsupported (R2) and supported (R5) Ru 2 cluster, the geometry optimization and energy calculation were performed with their spin multiplicities of 1, 3, 5, 7, and 9.A species having a quintet (S = 5) or heptet (S = 7) state is much more stable than it having a singlet, triplet, or nonet state.An unsupported Ru 2 cluster has a heptet ground state, i.e., 7 Ru 2 .Figure 6a shows the optimized geometries of the key species involved in the reaction between NH 3 and an unsupported 7 Ru 2 cluster (R2) through the MFP.By comparing between the structures shown in Figures 2e and 6a, it is interesting to identify that, on an Ru 2 cluster, when the N atom approaches one Ru atom, the detaching H atom, H a , approaches the two Ru atoms at the same time during the N-H bond activation process.Finally, the NH 2 fragment is attached to one Ru atom, and H a is attached to two Ru atoms to form a trigonal H. ..Ru. ..Ru structure in 7 IM2-Ru 2 -unsup.
cies involved in the reaction between NH3 and an unsupported 7 Ru2 cluster (R2) through the MFP.By comparing between the structures shown in Figures 3d and 6a, it is interesting to identify that, on an Ru2 cluster, when the N atom approaches one Ru atom, the detaching H atom, Ha, approaches the two Ru atoms at the same time during the N-H bond activation process.Finally, the NH2 fragment is attached to one Ru atom, and Ha is attached to two Ru atoms to form a trigonal H…Ru…Ru structure in 7 IM2-Ru2-unsup.From Figure 6b, it can be seen that the involvement of support significantly changes the stable structure of IM1 and IM2.The incorporation of the support makes 5 IM1-Ru2- From Figure 6b, it can be seen that the involvement of support significantly changes the stable structure of IM1 and IM2.The incorporation of the support makes 5 IM1-Ru 2 -BN stabilized in a structure that is closer to the transition state, 5 TS-Ru 2 -BN.The BN support also changes the position of H a in 7 IM2-Ru 2 -unsup, forming a structure with the NH 2 fragment and H a being at the same side, and H a is closer to Ru-a than to Ru-b, as shown in Figure 6b.
Figure 6c shows the energy profile for activation process with the MFP on the Ru 2unsup cluster (R2).The SM of this reaction has a heptet ground state, and as the reaction proceeds, the energy of the reaction system is decreased by 20.1 kcal/mol to reach the first energy minimum, 5 IM1-Ru 2 -unsup.With the low-energy spin transition, the barrier required for 5 IM1-Ru 2 -unsup to proceed to the most favorable TS, 3 TS-Ru 2 -unsup, is 20.6 kcal/mol.Finally, with another spin transition, the energy decreases by 30.2 kcal/mol to reach the second energy minimum of 5 IM2-Ru 2 -unsup.Figure 6d shows the energy profile for an activation process with the MFP on the Ru 2 -BN cluster (R5).A comparison between the last two panels in Figure 6 shows that the involvement of the BN support leads to a slight increase of 1.0 kcal/mol in the reaction energy barrier.The reaction energy of the elementary step decreases by 3.4 kcal/mol.The reaction barrier of (R5), i.e., the energy difference between 5 IM1-Ru 2 -BN and 5 TS-Ru 2 -BN is 21.5 kcal/mol, which is also consistent with 0.830 eV (19.1 kcal/mol) for CNT-supported Ru 2 , as reported by Zhou et al. [33].

Support Effect on the First N-H Bond Activation Process of NH 3 on an Ru 3 Cluster
Similar to the results about Ru 1 and Ru 2 shown in Sections 2.2 and 2.3, respectively, for all key species involved in the NH 3 activation process on an unsupported (R3) and supported (R6) Ru 3 cluster, the geometry optimization and energy calculation were performed with their spin multiplicities of 1, 3, 5, 7, 9, and 11.A species having a nonet (S = 9) state is significantly more stable than one with another spin state.An unsupported Ru 3 cluster has a nonet ground state, i.e., 9 Ru 3 .Figure 7a illustrates the optimized geometries of the key species involved in the reaction between NH 3 and an unsupported 9 Ru 3 cluster through the MFP (R3).Comparing the structures shown in Figures 2e, 6a and 7a, it can be seen that on an Ru 3 cluster, similar to the cases of Ru 1 and Ru 2 , when the N atom approaches one Ru atom, the detaching H atom, H a approaches one of the Ru atoms at the same time during the N-H bond activation process.Finally, the NH 2 fragment is attached to one Ru atom, and H a is attached to two Ru atoms to form a trigonal H. ..Ru. ..Ru structure in 9 IM2-Ru 3 -BN, similar as the Ru 2 case.Figure 7a,b shows that the involvement of the BN support changes the structure of TS by changing the position of Ha atom, from being roughly at the same plane with three Ru atoms to being out of the plane.The involvement of BN also slightly changes the structure of IM2.
Figure 7c shows the energy profile for the N-H bond activation process through the MFP on the Ru3-unsup cluster (R3).The SM of this reaction has a nonet ground state, 9 SM-Ru3-unsup, and as the reaction proceeds, the energy of the reaction system is decreased by 32.5 kcal/mol to reach the first energy minimum, 9 IM1-Ru3-unsup.As the reaction continues, the energy barrier required for 9 IM1-Ru3-unsup to proceed to 9 TS-Ru3unsup is 27.9 kcal/mol.Finally, the energy decreases by 35.7 kcal/mol to reach the second energy minimum, 9 IM2-Ru3-unsup.Figure 7d shows the energy profile for the activation process with MFP on the Ru3-BN cluster (R6).From the last two panels in Figure 7, the involvement of the BN support leads to a slight decrease of 0.9 kcal/mol in the reaction Figure 7a,b shows that the involvement of the BN support changes the structure of TS by changing the position of H a atom, from being roughly at the same plane with three Ru atoms to being out of the plane.The involvement of BN also slightly changes the structure of IM2.
Figure 7c shows the energy profile for the N-H bond activation process through the MFP on the Ru 3 -unsup cluster (R3).The SM of this reaction has a nonet ground state, 9 SM-Ru 3 -unsup, and as the reaction proceeds, the energy of the reaction system is decreased by 32.5 kcal/mol to reach the first energy minimum, 9 IM1-Ru 3 -unsup.As the reaction continues, the energy barrier required for 9 IM1-Ru 3 -unsup to proceed to 9 TS-Ru 3 -unsup is 27.9 kcal/mol.Finally, the energy decreases by 35.7 kcal/mol to reach the second energy minimum, 9 IM2-Ru 3 -unsup.Figure 7d shows the energy profile for the activation process with MFP on the Ru 3 -BN cluster (R6).From the last two panels in Figure 7, the involvement of the BN support leads to a slight decrease of 0.9 kcal/mol in the reaction energy barrier.The reaction energy of the elementary step decreases by −5.5 kcal/mol.In order to better understand the role of the BN support with different Ru cluster sizes, the relative energy and relative free energy at 298.15 K and 673.15K of all the key species involved in the MFP of the six reactions studied in this work are collected in Figure 8, their corresponding SMs being chosen as the energetic reference.Based on Figure 8, the support effect on the thermodynamic aspect, kinetic aspect, and the size effect aspect can be more clearly seen.8, the support effect on the thermodynamic aspect, kinetic aspect, and the size effect aspect can be more clearly seen.

Thermodynamic Aspect of Support Effect
The incorporation of BN favors the stability of IM1 and TS for the Ru1 and Ru2 clusters, and disfavors the stability of IM1 and TS for the Ru3 cluster.Compared to the Ru1 case, the stability of these two states is less favored by BN support for the Ru2 case.From the reaction energy point of view, formation of IM2 from SM is favored by the incorporation of BN for all Run clusters.

Kinetic Aspect of Support Effect
Based on the transition state theory, the relationship between the rate constant (k) and the molar Gibbs free energy of activation (ΔG ≠ ) is expressed as [34] where kB is the Boltzmann constant, h is the Planck constant, T is the reaction temperature, and R is the universal gas constant.Since this paper focuses on the support effect and the relative free energy for two similar reactions can be more reliable than the absolute free energy profile for one reaction with the state-of-the-art DFT calculation, the relative rate constant of the supported case over that of the unsupported case was calculated in this work.From Equation ( 1), the following equation can be easily derived:

Thermodynamic Aspect of Support Effect
The incorporation of BN favors the stability of IM1 and TS for the Ru 1 and Ru 2 clusters, and disfavors the stability of IM1 and TS for the Ru 3 cluster.Compared to the Ru 1 case, the stability of these two states is less favored by BN support for the Ru 2 case.From the reaction energy point of view, formation of IM2 from SM is favored by the incorporation of BN for all Ru n clusters.

Kinetic Aspect of Support Effect
Based on the transition state theory, the relationship between the rate constant (k) and the molar Gibbs free energy of activation (∆G ̸ = ) is expressed as [34] where k B is the Boltzmann constant, h is the Planck constant, T is the reaction temperature, and R is the universal gas constant.Since this paper focuses on the support effect and the relative free energy for two similar reactions can be more reliable than the absolute free energy profile for one reaction with the state-of-the-art DFT calculation, the relative rate constant of the supported case over that of the unsupported case was calculated in this work.From Equation ( 1), the following equation can be easily derived: In Equation ( 2), the left side term is the relative rate constant, and the subscripts "BN-sup" and "unsup" stand for the reactions involving and not involving the model support, respectively.∆G ̸ = can be calculated from the relative free energy of TS over IM1 for all the reactions of (R1)~(R6).We calculated the relative rate constants at two temperatures of 298.15K and 673.15 K, since the former is widely concerned in general physical chemistry [35], and the latter is a typical temperature for Ru-catalyzed NH 3 decomposition to H 2 in practice [4,12,15,24].By collecting the free energy data at 298.15 and 673.15K (Table 2) for all of the TSs and IM1s in this work, and based on Equation (2), the relative rate constants, k BN-sup /k unsup , can be easily calculated as 20.1, 2.8, and 3.2 for Ru 1 , Ru 2 , and Ru 3 clusters, respectively, at 298.15 K.These k BN-sup /k unsup values are 775, 9.4, and 272 for Ru 1 , Ru 2 , and Ru 3 cases, respectively, at 673.15 K.The calculated data indicate that the involvement of the model BN support leads to a great influence on the reaction rate constant for N-H bond activation, especially for the single atom Ru catalyst, and at high reaction temperatures.Our previous works studied the silica support effect on the C-H bond activation of ethane on a nickel oxide cluster [36].In that work, the energy of activation of C-H bond activation of ethane on a nickel oxide cluster is increased (instead of decrease in this paper) by the involvement of the silica support.Cao et al. studied the support effect on the Pdcatalyzed semi-hydrogenation of acetylene from the structural and kinetic perspectives [37].They found that, compared with Al 2 O 3 , the CNT support reduced the Pd 0 3d binding energy and suppressed the formation of PdH x species to enhance the reaction kinetics in terms of the ethylene selectivity and formation rate.These different effects on the energy of activation (consequently the reaction rate constant) may be caused by the difference of the support nature, and the computational study like this work can help researchers in the rational selection of good catalytic supports.
The existing literature, exemplified by a review article of ref. [38], clearly indicates that the catalytic support significantly influences the efficiency of the NH 3 decomposition for hydrogen production.Compared to traditional oxide supports (such as alumina and magnesium oxide), Ru catalysts supported on novel carbon materials (e.g., graphene) exhibit a markedly superior performance [39,40].Due to the complexity of the ammonia decomposition reaction mechanism, it remains unclear how supports accelerate the entire decomposition process.Nevertheless, our research results suggest that the inclusion of a carbon analogue support, h-BN, can accelerate the first (and certainly crucial) step of the N-H bond activation (see k BN-sup /k unsup values shown above).The theoretically predicted trends of acceleration are qualitatively aligned with the trends observed in ammonia decomposition reactions involving graphene (h-BN analogue) as the catalytic support.

Cluster Size Effect
Combining the findings described in Sections 2.5.1 and 2.5.2, one can have a different view angle of the cluster size effect.For the unsupported cases, with using the SM as the energetic reference, the stability of either IM1 or IM2 increases with the order of Ru 1 < Ru 2 < Ru 3 .The involvement of BN makes the stability order for the IM1 case changes to the order of Ru 1 > Ru 2 > Ru 3 , with the stability of IM2 still maintaining the order of Ru 1 < Ru 2 < Ru 3 .
In the kinetic aspect, the free energy of activation follows an increasing order of Ru 2 < Ru 1 < Ru 3 , for both of the unsupported and supported cases, and thus the theoretical rate constant follows the decreasing order of Ru 2 > Ru 1 > Ru 3 .However, the degree of influence on the reaction rate constant induced by the BN support follows the order of Ru 1 > Ru 3 > Ru 2 .

Support Effect on the Electron Transfer from IM1 to TS
Table 3 shows the NBO charge changes of different moieties for the process of IM1 going to TS.During the IM1 → TS process, Ru n clusters undergo electron loss, while NH 2 fragments containing hydrogen atoms (H a ) experience electron gain.During the transformation from IM1 to TS in all six cases in this work, there is a loss of charge in the Ru atom/cluster.For the Ru 1 system, upon introducing the BN support, the charge lost amount of the Ru atoms during the IM1→TS transformation noticeably decreases (from 0.418 to 0.086, see Table 3).Simultaneously, the BN support loses 0.159 of its charge.It is not difficult to speculate that the BN support shares a portion of the charge loss with the Ru atoms.For the Ru 2 and Ru 3 cases, upon introducing the support, the charge lost amount of the Ru atoms during the IM1→TS process slightly increases.Table 3 also indicates that the BN support has only a slight charge change (Ru 2 -BN, 0.025; Ru 3 -BN, −0.047).It no longer directly assists in the charge transfer of Ru atoms.A possible reason is that the distance between the activation sites in Ru 2 /Ru 3 clusters and the BN support increases compared to the Ru 1 case.
During the IM1→TS process, the H a atom gains electron for all six cases.The involvement of the BN support leads to a decrease in the electron gain for the H a atom.At the same time, as can be seen in Table 2, the involvement of the BN support leads to a decrease in N-H bond activation free energy.Putting the results of NBO analysis and the reaction energy barrier together, one can further find that the trend in the electron transfer of H a is consistent with the change of reaction energy barrier.The decrease in the reaction barrier introduced by the BN support can be associated with its electron transfer behavior.

Support Effect on the Spin Conversion Behavior for the MFPs
Table 4 shows the spin multiplicity of intermediates and transition states in the MFP on the Ru n -unsup and Ru n -BN clusters.The main changes for the spin states introduced by the incorporation of the BN support are as follows.Firstly, Table 4 shows that the ground states of all SM conform to a regular pattern, with the most favorable spin multiplicity being 2n + 3 where "n" is the number of Ru atoms.The involving BN support does not change the ground states of the metal clusters.Second, the changes of the spin multiplicity of the intermediate and transition state in the MFP by the BN support is shown by the fact that the most favorable spin multiplicity is not changed for the n = 1 and 3 cases, and the most favorable spin multiplicity is changed for the n = 2 case.No spin transition occurs at the Ru 3 cases.Finally, the involving BN support changes the spin multiplicity of IM1 and IM2 at n = 2, from 7 IM1 to 5 IM1 and from 7 IM2 to 7 IM2.The current literature shows that the reaction of NH 3 decomposition to generate H 2 at low temperatures is unsatisfactory.Based on the data obtained, it is reasonable to speculate that the reaction requires high temperatures to induce the transition of the spin states in the intermediates and transition states.When the energies of the two spin states are close, various external perturbations like temperature, pressure, and magnetic field can induce the spin state transition or crossover [41].The spin state of the transition metal affects the magnetization strength and thermal conductivity of the material to change the thermoelectric properties of the material [42].Inspection of the spin state data in Table 4 data shows that the state crossover occurs in most cases.So, it is reasonable to speculate that a suitable support may help improve the N-H bond activation rate during NH 3 decomposition to generate H 2 at low temperatures.In the long term, with the aid of computational tools, the findings in this paper will provide a promising direction for designing a good catalyst for H 2 generation from NH 3 decomposition at low temperatures.

Preliminary Orbital Analysis
In principle, the ground spin multiplicity of a certain species can be explained by the relative energy of the frontier orbitals of this species, namely the highest occupied molecular orbital (HOMO), the singly occupied molecular orbital(s) (SOMO), and the lowest unoccupied molecular orbital (LUMO).In order to better understand the spin transition behavior of some key species involved in the N-H bond activation processes in this work, in the preliminary stage we focused on understanding the ground spin multiplicity of 5 SM-Ru1-unsup, 3 IM-Ru1-unsup, 5 SM-Ru1-BN, and 3 IM-Ru1-BN.Figure 9 shows the relative energy/energy split of the HOMO, SOMO, and LUMO of these four species as well as their orbital contours.Since NH 3 is a singlet species, the orbital image of NH 3 is not shown for the SMs.It is well known that an Ru atom has a quintet state, that is, having four singly occupied electrons.Figure 9a shows SOMO-1~3 orbitals of 5 SM-Ru1-unsup (actually an Ru atom) having Ru 4d characters are nearly degenerated, and SOMO-4 having Ru 5s character.The energy split between this Ru 5s orbital and Ru 4d in SOMO-3 is 0.11 atomic unit (a.u.). Figure 9b shows the approaching of NH 3 to Ru to form 3 IM-Ru1-unsup, making the energy split of this Ru 5s orbital over the Ru 4d orbital significantly increased (energy split of 0.21 a.u), and thus the electron in SOMO-4 in 5 SM-Ru1-unsup tend to occupy SOMO-1 to form an electron pair.Therefore, SOMO-1 in 5 SM-Ru1-unsup changes to a new HOMO ′ in 3 IM-Ru1-unsup, making it having a triplet ground state.
Figure 9c shows that when a BN support approaches the Ru atom to form SM-Ru 1 -BN, the energy split of the Ru 5s orbital with the Ru 4d orbital in SOMO-3 is only 0.10 a.u., making SOMO-4 still being occupied by an electron in SM-Ru 1 -BN, thus having a quintet state.A similar reason for why IM1-Ru 1 -BN having a triplet ground state can be found compared to the case of IM1-Ru1-unsup according to the energy values shown in Figure 9d.For the relative orbital energies, the HOMO energy is selected as the energetic reference (0 atomic unit, a.u.).Since NH3 is a singlet species, the orbital image of NH3 is not shown for the SMs.
Figure 9c shows that when a BN support approaches the Ru atom to form SM-Ru1-BN, the energy split of the Ru 5s orbital with the Ru 4d orbital in SOMO-3 is only 0.10 a.u., making SOMO-4 still being occupied by an electron in SM-Ru1-BN, thus having a quintet state.A similar reason for why IM1-Ru1-BN having a triplet ground state can be found compared to the case of IM1-Ru1-unsup according to the energy values shown in Figure 9d.

Computational Methods and Reactant Models
The DFT calculations were performed by employing the M062X [43] exchange and correlation functionals to explore the potential energy surfaces (PESs) of the first N-H bond activation process of NH3.To better describe the long-term interaction between NH3 and Ru or BN nanosheet due to a dispersion problem, the Grimme's D3 dispersion correction [44] was applied for all DFT calculations.The activation process operates on the Run (n = 1, 2, 3) clusters without and with B19N19H16 as the model BN support [33].This For the relative orbital energies, the HOMO energy is selected as the energetic reference (0 atomic unit, a.u.).Since NH 3 is a singlet species, the orbital image of NH 3 is not shown for the SMs.

Computational Methods and Reactant Models
The DFT calculations were performed by employing the M062X [43] exchange and correlation functionals to explore the potential energy surfaces (PESs) of the first N-H bond activation process of NH 3 .To better describe the long-term interaction between NH 3 and Ru or BN nanosheet due to a dispersion problem, the Grimme's D3 dispersion correction [44] was applied for all DFT calculations.The activation process operates on the Ru n (n = 1, 2, 3) clusters without and with B 19 N 19 H 16 as the model BN support [33].This model support is denoted as "-BN" appearing in a certain species notation hereafter in this paper.M062X is known to be able to provide a good description of the PES for the bond activation process on transition metal clusters [34,45] as well as for the BN-involved reaction system [46].
In the present status, although DFT cannot easily provide a quantitative explanation of the experimental data, the relative reaction barrier is much more credible [47].The basis information set will be specified after the description of the model of reactants.All PESs were explored by optimizing the geometries in the energy minimums for the reactants, the intermediates, and the products, and the first-order saddle points for transition states using the Gaussian 09 program suite (B.09 (for initial optimization) and C.01 (for final optimization and frequency analysis) versions [48,49]).Frequency analyses were performed to confirm the energy minimums and the first-order saddle points, as well as to obtain the zero-point corrected energies of the optimized geometries.Intrinsic reaction coordinate (IRC) computations [50] were performed to confirm the transition states connecting the appropriate reactants and products.
Since this paper emphasizes an understanding of the support effect of a model BN on the N-H bond activation, we investigated and compared the structural and energetic data for the interaction of supported and unsupported Ru metal clusters with one NH 3 molecule.In order to directly understand the role of model BN support, all of the 6 reactions interested in this paper are categorized into two types, and expressed as follows.
The first type corresponds to the unsupported cases, i.e., the reaction of NH 3 with an unsupported Ru n cluster (where n = 1, 2, or 3) to form the NH 2 -Ru n -H species, which includes the following three reactions: The second type corresponds to the supported cases, i.e., the reaction between NH 3 and model BN-supported Ru n cluster (denoted as Ru n -BN, where n = 1, 2, 3) to afford NH 2 -Ru n -H-BN species, which includes the following three reactions in detail: For the above 6 reactions, the key species on different PESs with a certain spin multiplicity (S) were optimized in geometries and energetically calculated.For easy description hereafter in this paper, the notations for different key species on different PESs are defined as in the following regulations.
Firstly, these key species include the starting materials (SM), the first intermediate formed from the SM, IM1, the transition state followed by IM1, TS, and the second intermediate followed by TS, IM2.The SM is actually the system of separated NH 3 and one of the six Ru clusters in the left side of (R1)~(R6), and IM2 is actually the first N-H bond activation product of one of (R1)~(R6).Secondly, since all species in all of the six reactions have an even number of electrons, the PESs with different multiplicities of S = 1, 3, 5, 7. . .(i.e., singlet, triplet, quintet, heptet, and so on) were explored.The information about S is put in the upper-left superscript in front of a species notation to indicate its spin multiplicity.For example, 7 Ru 3 is a heptet Ru 3 cluster, and 3 TS is a triplet transition state.Therefore, possibly the most complicated notation for a certain species in this paper can be expressed as S (SM, IM1, TS, or IM2)-Ru n -(unsup or BN), where the suffix "-unsup" stands for the unsupported case, and "-BN" stands for the model BN-supported cases.For example, 7 IM2-Ru 3 -BN means the IM2 from the reaction of NH 3 with a model BN-supported Ru 3 cluster with a heptet state, and 3 TS-Ru 2 -unsup means the TS in the reaction of NH 3 with an unsupported Ru 2 cluster with a triplet state under the above name regulation.
Figure 10 shows the M06X-GD3 optimized geometries of the B 19 N 19 H 16 sheet and 5 Ru 1 -BN (c) in different views.For B 19 N 19 H 16 , the 6-311G** basis set was used for atoms in the red circles as indicated in Figure 10a,c.The 6-31G basis set was used for the residual atoms of B 19 N 19 H 16 .Two levels of basis sets were used for describing the model BN support in order to compromise between the computational accuracy and the time expense.The SDD basis set was used for the Ru atoms [51].The 6-311G** basis set was also used for N and H atoms in NH 3 .The cluster model was used for the calculations in this work.For all of the structure optimization and energy calculations, all of the atoms were allowed to relax.Hereafter in this paper, for all the geometries in the supported cases, only the side view of the BN support will be shown in Section 2 unless specially specified.
Ru3 cluster with a heptet state, and 3 TS-Ru2-unsup means the TS in the reaction of NH3 with an unsupported Ru2 cluster with a triplet state under the above name regulation.
Figure 10 shows the M06X-GD3 optimized geometries of the B19N19H16 sheet and 5 Ru1-BN (c) in different views.For B19N19H16, the 6-311G** basis set was used for atoms in the red circles as indicated in Figure 10a,c.The 6-31G basis set was used for the residual atoms of B19N19H16.Two levels of basis sets were used for describing the model BN support in order to compromise between the computational accuracy and the time expense.The SDD basis set was used for the Ru atoms [51].The 6-311G** basis set was also used for N and H atoms in NH3.The cluster model was used for the calculations in this work.For all of the structure optimization and energy calculations, all of the atoms were allowed to relax.Hereafter in this paper, for all the geometries in the supported cases, only the side view of the BN support will be shown in Section 2 unless specially specified.

Conclusions
To gain deeper insight into the influence of a BN support on the N-H bond activation reaction, the optimized geometries and energetics calculated with the DFT method for the first N-H bond activation of NH3 on unsupported Run clusters and on Run-BN clusters were compared.This DFT study provides the following primary conclusions: (1) From a geometric standpoint, the incorporation of the BN support does not lead to obvious alterations of the structure of the intermediates and transition states involved in the most favorable pathway (MFP).This is mainly reflected by slight changes in the distance between the Ha and N atoms in NH3 in the TSs, IM1s, and IM2s when the unsupported and BN-supported cases are compared.
(2) Considering thermodynamics, the formation of IM2 is favored by the presence of the BN support for all Run clusters.In contrast, the formation of IM1 is favored for the Ru1 and Ru2 cases, and disfavored for the Ru3 case by the presence of BN.
(3) In terms of kinetics, the incorporation of the BN support leads to a decrease in the free energy of activation of the first N-H bond activation process of NH3, and thus can improve the reaction rate constant.The rate constant improvement induced by the BN support is more significant at high temperatures.

Conclusions
To gain deeper insight into the influence of a BN support on the N-H bond activation reaction, the optimized geometries and energetics calculated with the DFT method for the first N-H bond activation of NH 3 on unsupported Ru n clusters and on Ru n -BN clusters were compared.This DFT study provides the following primary conclusions: (1) From a geometric standpoint, the incorporation of the BN support does not lead to obvious alterations of the structure of the intermediates and transition states involved in the most favorable pathway (MFP).This is mainly reflected by slight changes in the distance between the H a and N atoms in NH 3 in the TSs, IM1s, and IM2s when the unsupported and BN-supported cases are compared.
(2) Considering thermodynamics, the formation of IM2 is favored by the presence of the BN support for all Ru n clusters.In contrast, the formation of IM1 is favored for the Ru 1 and Ru 2 cases, and disfavored for the Ru 3 case by the presence of BN.
(3) In terms of kinetics, the incorporation of the BN support leads to a decrease in the free energy of activation of the first N-H bond activation process of NH 3 , and thus can improve the reaction rate constant.The rate constant improvement induced by the BN support is more significant at high temperatures.
(4) Spin transition occurs in the MFP in (R1), (R2), (R4) and (R5) for the Ru 1 and Ru 2 cases, and no spin transition occurs in the MFP in (R3) and (R6) for the Ru 3 cases.The incorporation of the BN support changes the spin transition behavior for the Ru 2 cluster during the first N-H bond activation of NH 3 .
The spin transition behavior connecting to the single and gemini-Ru atom catalysts underscores the importance of considering spin transition behavior when choosing catalytic supports, particularly in the field of single atom catalysis.
Our study contributes to a deeper understanding of the N-H bond activation process in catalytic NH 3 decomposition.These insights offer valuable guidance for selecting more favorable catalytic supports in order to synthesize better catalysts.We will continue to carry out further works to provide better theoretical guidance for the design of efficient catalysts for H 2 production via NH 3 decomposition.

Molecules 2024 , 21 Figure 2 .
Figure 2. Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH3 on unsupported Ru1 ((R1) with suffix of -Ru1-unsup) and the model BN-supported Ru1 ((R4) with suffix of -Ru1-BN).Panels (a,b) illustrate the unsupported cases on the quintet and triplet PES, respectively, while (c,d) demonstrate the supported cases on the quintet and triplet PES.Panel (e) shows the cases of (R1) with the most favorable pathway (MFP), and (f) for (R4).All distances are indicated in Å.

Figure 2 .
Figure 2. Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH 3 on unsupported Ru 1 ((R1) with suffix of -Ru 1 -unsup) and the model BN-supported Ru 1 ((R4) with suffix of -Ru 1 -BN).Panels (a,b) illustrate the unsupported cases on the quintet and triplet PES, respectively, while (c,d) demonstrate the supported cases on the quintet and triplet PES.Panel (e) shows the cases of (R1) with the most favorable pathway (MFP), and (f) for (R4).All distances are indicated in Å.
is noteworthy that the intermediate IM1 has a triplet ground state rather than quintet.In another word, the ground spin state of Ru is changed during the course of an NH 3 molecule approaching an Ru atom.More importantly, both the transition state TS and intermediate IM2 display lower energy on the triplet PES compared to the quintet PES.The activation energy of (R1), defined as the energy difference between TS-Ru 1 -unsup and IM1-Ru 1 -unsup, is also lower on the triplet PES (25.6 kcal/mol) than on the quintet PES (38.8 kcal/mol).

Figure 3 .
Figure 3. Shown is the relative energy profiles for the first N-H bond activation of NH3 on one Ru atom for the unsupported ((R1) with suffix of -Ru1-unsup) and supported ((R4) with suffix of -Ru1-BN).The relative energy profiles on the triplet (green) and quintet (blue) PESs are included in panel (a) for (R1) and in panel (b) for (R4).on Ru1-unsup (a) and Ru1-BN (b).The relative energy profiles of the most favorable pathway (MPF) are shown in panel (c) for (R1) and in panel (d) for (R4).

Figure 3 .
Figure 3. Shown is the relative energy profiles for the first N-H bond activation of NH 3 on one Ru atom for the unsupported ((R1) with suffix of -Ru 1 -unsup) and supported ((R4) with suffix of -Ru 1 -BN).The relative energy profiles on the triplet (green) and quintet (blue) PESs are included in panel (a) for (R1) and in panel (b) for (R4).on Ru 1 -unsup (a) and Ru 1 -BN (b).The relative energy profiles of the most favorable pathway (MPF) are shown in panel (c) for (R1) and in panel (d) for (R4).

Figure 4 .
Figure 4. Shown is a simple schematic illustration for the landscape of the energy surface near the energy minimum of triplet and quintet IM1-Ru1-unsup in (R1).Point a, the energy minimum on the triplet PES, represents the energy of optimized 3 IM1-Ru1-unsup.Point a′ represents the energy of IM1-Ru1-unsup in quintet state while having the same geometry as point a.The energy difference between a and a′ is the Frank-Condon excitation energy (EFC) at point a.Point b represents the geometry and the energy of 3 IM1-Ru1-unsup where the spin transition occurs with the largest probability.The energy difference between b and b′ represents the minimum energy at cross point (MECP).Point c is the energy of optimized 5 IM1-Ru1-unsup.Point c′ represents the energy of IM1-Ru1-unsup in triplet state while having the same geometry as point c.The energy difference between c and c′ is the EFC at point c, with the geometry of optimized 5 IM1-Ru1-unsup.

Figure 4 .
Figure 4. Shown is a simple schematic illustration for the landscape of the energy surface near the energy minimum of triplet and quintet IM1-Ru 1 -unsup in (R1).Point a, the energy minimum on the triplet PES, represents the energy of optimized 3 IM1-Ru 1 -unsup.Point a ′ represents the energy of IM1-Ru 1 -unsup in quintet state while having the same geometry as point a.The energy difference between a and a ′ is the Frank-Condon excitation energy (E FC ) at point a.Point b represents the geometry and the energy of 3 IM1-Ru 1 -unsup where the spin transition occurs with the largest probability.The energy difference between b and b ′ represents the minimum energy at cross point (MECP).Point c is the energy of optimized 5 IM1-Ru 1 -unsup.Point c ′ represents the energy of IM1-Ru 1 -unsup in triplet state while having the same geometry as point c.The energy difference between c and c ′ is the E FC at point c, with the geometry of optimized 5 IM1-Ru 1 -unsup.

Figure 5
Figure 5 show the optimized geometries of IM1 and TS involved in the first N-H bond activation of NH 3 on the varied model BN-supported Ru 1 ((R4) with different sizes of BN model sheet).To examine the rationality of the B 19 N 19 H 16 sheet as a representative model BN sheet, we examined how the reaction barrier of (R4), i.e., energy difference of

Figure 5 .
Figure 5. Shown are the optimized geometries of IM1 and TS involved in the first N-H bond activation of NH3 on the varied model BN-supported Ru1 ((R4) with different sizes of BN model sheet).(a) 3 IM1-Ru1-BN with a B26N26H18 model in vertical view, (b) 3 IM1-Ru1-BN with a B26N26H18 model in side view, (c) 3 TS-Ru1-BN with a B26N26H18 model in side view, (d) 3 IM1-Ru1-BN with a B15N15H14 model in vertical view, (e) 3 IM1-Ru1-BN with a B15N15H14 model in side view, and (f) 3 TS-Ru1-BN with a B15N15H14 model in side view.

Figure 5 .
Figure 5. Shown are the optimized geometries of IM1 and TS involved in the first N-H bond activation of NH 3 on the varied model BN-supported Ru 1 ((R4) with different sizes of BN model sheet).(a) 3 IM1-Ru 1 -BN with a B 26 N 26 H 18 model in vertical view, (b) 3 IM1-Ru 1 -BN with a B 26 N 26 H 18 model in side view, (c) 3 TS-Ru 1 -BN with a B 26 N 26 H 18 model in side view, (d) 3 IM1-Ru 1 -BN with a B 15 N 15 H 14 model in vertical view, (e) 3 IM1-Ru 1 -BN with a B 15 N 15 H 14 model in side view, and (f) 3 TS-Ru 1 -BN with a B 15 N 15 H 14 model in side view.These calculations unequivocally demonstrate that the BN models used in this work possess size consistency, thus validating the rationale behind utilizing the B 19 N 19 H 16 sheet model for BN support calculations.Considering the computational complexity of this work, we ultimately opted for the B 19 N 19 H 16 sheet model as the BN support for the following calculations.

Figure 6 .
Figure 6.Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH3 on unsupported Ru2 ((R2) with suffix of -Ru2-unsup) and the model BN-supported Ru2 ((R5) with suffix of -Ru2-BN) cluster and their relative energy profiles.Panel (a) is for (R2) with the most favorable pathway (MFP), and (b) for (R5) with the most favorable pathway (MFP).The key distances are indicated in Å.The two Ru atoms are named as Ru-a (indicated with *) and Ru-b in this part for more convenient elaboration.Panels (c,d) are the relative energy profiles for the first N-H bond activation of NH3 on an Ru2-unsup (R2) and on an Ru2-BN cluster (R5) with the most favorable pathway (MFP).

Figure 6 .
Figure 6.Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH 3 on unsupported Ru 2 ((R2) with suffix of -Ru 2 -unsup) and the model BN-supported Ru 2 ((R5) with suffix of -Ru 2 -BN) cluster and their relative energy profiles.Panel (a) is for (R2) with the most favorable pathway (MFP), and (b) for (R5) with the most favorable pathway (MFP).The key distances are indicated in Å.The two Ru atoms are named as Ru-a (indicated with *) and Ru-b in this part for more convenient elaboration.Panels (c,d) are the relative energy profiles for the first N-H bond activation of NH 3 on an Ru 2 -unsup (R2) and on an Ru 2 -BN cluster (R5) with the most favorable pathway (MFP).

Molecules 2024 , 21 Figure 7 .
Figure 7. Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH3 on unsupported Ru3 ((R3) with suffix of -Ru3-unsup) and the model BN-supported Ru3 ((R6) with suffix of -Ru3-BN) cluster and their relative energy profiles.Panel (a) is for (R3) with the most favorable pathway (MFP), and (b) for (R6) with the MFP.The Ru atom indicated with "*" is close to the N atom in NH3.Panels (c,d) are the relative energy profiles for the first N-H bond activation of NH3 on an Ru3-unsup (R3) and on an Ru3-BN cluster (R6) with the most favorable pathway (MFP).

Figure 7 .
Figure 7. Shown are the optimized geometries of the key species involved in the first N-H bond activation of NH 3 on unsupported Ru 3 ((R3) with suffix of -Ru 3 -unsup) and the model BN-supported Ru 3 ((R6) with suffix of -Ru 3 -BN) cluster and their relative energy profiles.Panel (a) is for (R3) with the most favorable pathway (MFP), and (b) for (R6) with the MFP.The Ru atom indicated with "*" is close to the N atom in NH 3 .Panels (c,d) are the relative energy profiles for the first N-H bond activation of NH 3 on an Ru 3 -unsup (R3) and on an Ru 3 -BN cluster (R6) with the most favorable pathway (MFP).

2. 5 .
Further Discussion on the Support Effect for the First N-H Bond Activation of NH 3 on Ru n (n = 1, 2, 3) Clusters

Figure 8 .
Figure 8. Relative energy of all key species involved in the MFP of the first N-H bond activation of NH3 on unsupported and BN-supported Run (n = 1, 2, 3) clusters, as expressed by (R1)~(R6).

Figure 8 .
Figure 8. Relative energy of all key species involved in the MFP of the first N-H bond activation of NH 3 on unsupported and BN-supported Ru n (n = 1, 2, 3) clusters, as expressed by (R1)~(R6).

Molecules 2024 , 21 Figure 9 .
Figure 9.The molecular orbital contours and the relative orbital energy (in atomic unit, a.u.) of some selected frontier orbitals (see the text for detail) of 5 SM-Ru1-unsup (a), 3 IM-Ru1-unsup (b), 5 SM-Ru1-BN (c), and 3 IM-Ru1-BN (d).For the relative orbital energies, the HOMO energy is selected as the energetic reference (0 atomic unit, a.u.).Since NH3 is a singlet species, the orbital image of NH3 is not shown for the SMs.

Figure 10 .
Figure 10.Vertical (a) and side (b) views of the model BN of a B19N19H16 sheet, and the 5 Ru1-BN model (c).The Ru atom is located close to the indicated N atom with a distance of 3.562 Å.For the B and N atom in the cycle, a high level basis set of 6-311G** was used for calculation as described in the text.Color for each atoms: N (blue), H (white), Ru (green), and B (pink); see the inset over panel (b).

( 4 )
Spin transition occurs in the MFP in (R1), (R2), (R4) and (R5) for the Ru1 and Ru2 cases, and no spin transition occurs in the MFP in (R3) and (R6) for the Ru3 cases.The incorporation of the BN support changes the spin transition behavior for the Ru2 cluster during the first N-H bond activation of NH3.

Figure 10 .
Figure 10.Vertical (a) and side (b) views of the model BN of a B 19 N 19 H 16 sheet, and the 5 Ru 1 -BN model (c).The Ru atom is located close to the indicated N atom with a distance of 3.562 Å.For the B and N atom in the cycle, a high level basis set of 6-311G** was used for calculation as described in the text.Color for each atoms: N (blue), H (white), Ru (green), and B (pink); see the inset over panel (b).

Table 1 .
Adsorption energy (E ad ) and free energy at 298 K (G ad ) of an Ru n cluster on the BN support.All the spin multiplicity indicated on the upper left of a species notation corresponds to the ground spin state.

Table 2 .
Free energy of activations, ∆G ̸ = (in kcal/mol), at 298.15 and 673.15K for all the six N-H bond activation reactions (R1)~(R6) studied in this work.

Table 3 .
NBO charge change of different moieties between the most favorable IM1 and TS involved in the first N-H bond activation process of NH 3 on Ru

Table 4 .
Spin multiplicity of intermediates and transition states in most favorable pathways for the first N-H bond activation of NH 3 with and without the BN support.